The broad, long-term objective of this research is to understand how ion pumps operate in cell membranes while providing the energetics of the cell and healthy ionic balance. In pursuit of this long-term objective it is proposed to study the bacteriorhodopsin (bR) proton pump in the purple membrane of Halobacterium halobium which is more amenable to detailed analysis than most ion pumps. One of the primary pieces of information for studying the bacteriorhodopsin proton pump is an accurate phenomenological description of the sequence of events that take place after bR is activated by light. Such a description involves the identification of chemical intermediates about which it is important to obtain as much information as possible. The first main specific aim of this research is to obtain the correct description of the photocycle of bR by systematic global analysis of extensive time-resolved light absorption data sets recently obtained. Achievement of this aim will provide the spectra of the chemical intermediates in the photocycle whose spectral shifts and oscillator strengths can later be related to molecular models of the photocycle. Achievement of this aim will also provide a useful relationship between the quantum efficiencies and the molar extinction of the first intermediate. One step in the analysis requires analyzing linear dichroic absorption data which gives information about the motions of the bR chromophore. The second main aim is to develop the analytical tools to extract the intrinsic kinetic model from broad classes of time-resolved data. Such analytical tools should prove useful for other biophysical problems subject to non-linear constraints. For photocycle problems the constraint is that the spectra of the chemical intermediates are nearly independent of the temperature. The photocycle itself changes rapidly with temperature, thereby imprinting its signature on the temperature dependence of the data, but in a way which has not previously been decipherable.